Question

If cos x + sec x = -2, then for a positive integer n, cos"x + secºx is
a) 2
b) - 2
c)-2 if n is odd and 2 if n is even
d) - 2 if n is even and 2 if n is odd​

Answer 1

Answer:

given

cosx + secx = -2

cosx + 1/cosx = -2

cos^2x + 1 = -2 cosx

cos^2x + 2cosx + 1 = 0

(cosx + 1)^2 = 0

it is possible only when

cosx + 1 = 0

cosx = -1

so, secx = 1/cosx = 1/(-1) = -1

now,

cos^nx + sec^nx

= (-1)^n + (-1)^n

now if n is even, solution will be

1+1 = 2

if n is odd, solution will be

-1 -1 = -2

so option c